where \(E_0\)  is the ground-state energy and \(\mathcal {V}\)  the potential energy
along the most likely fission path as parametrized by the curvilinear abscissa
\(s\) . The quantity \(B(s)\)  is the collective inertia tensor that we have already
mentioned several time. The integrand in (REF ) is the classical
action, and it is integrated between the inner turning point \(s=a\)  and the
outer turning point \(s=b\) . The formula (REF ) requires a collective
space spanned by some variables \(\mathbf {q}\) , with a collective potential energy
\(\mathcal {V}(\mathbf {q})\)  and a collective inertia tensor \({B}(\mathbf {q})\) .
Since there are different models to compute these quantities (we mentioned the
ATDHFB and GCM+GOA models) there will be a strong dependency of the calculated
spontaneous fission half-lives on the model inputs – especially so since both
the potential and inertia enter as an exponent. For example, systematic
calculations show very large variations of \(\tau _{\rm SF}\)  depending on: (i)
the model used to compute the inertia (ATDHFB or GCM) and the accompanying
approximations (perturbative versus non-perturbative cranking)
[1]}, [2]} (ii) the model to compute the collective
energy \(\mathcal {V}\)  [3]} (iii) the type and number of collective
variables, especially the role of pairing correlations [4]}, [5]}, [6]}, (iv) the prescription for the ground-state energy
[7]}, [2]}.
<FIGURE>